1.设A,B皆为非空有界数集,定义数集A+B={z|z=x+y,x∈A,y∈B}.证明:(1)sup(A+B)=supA+supB;(2)inf(A+B)=infA+infB.2.设A,B皆为非空有界数集,且对任何x∈A,y∈B,都有x≥0,y≥0,定义数集AB={z|z=x·y,x∈A,y∈B}.证明:(1)supAB=supA·supB;(2)infAB=infA·infB.
1.设A,B皆为非空有界数集,定义数集A+B={z|z=x+y,x∈A,y∈B}.证明:(1)sup(A+B)=supA+supB;(2)inf(A+B)=infA+infB.2.设A,B皆为非空有界数集,且对任何x∈A,y∈B,都有x≥0,y≥0,定义数集AB={z|z=x·y,x∈A,y∈B}.证明:(1)supAB=supA·supB;(2)infAB=infA·infB.